Sound Waves: Characteristics and Applications

Why This Matters

Close your eyes for a moment and just listen. A fan whirring. A bus honking on the road. Someone calling your name from the next room. Birds outside. Without opening your eyes, you already know a lot about the world around you. That is the power of sound.

But here is a strange question. When your friend calls your name from across the room, nothing solid flies from their mouth into your ear. No ball, no string, no air rushing across to you. So what actually travels from them to you? What carries the message “your name” through all that empty-looking space?

And there are odder puzzles. Two astronauts floating side by side in space cannot hear each other shout, even though they are right next to each other. A bat flying in pitch darkness never crashes into walls. A ship far out at sea can measure exactly how deep the ocean is below it, without any rope. Shout near a hill and your own voice comes back to you a moment later.

All of these are about one thing: sound, and how it travels. By the end of this chapter you will know what sound really is, how it moves, why it sometimes cannot move at all, and how we use it to “see” things we cannot reach. None of it will be a mystery. You will know exactly why.

The Big Idea

Sound is made by vibrations — a quick to-and-fro shaking of an object. That shaking pushes and pulls the particles of the material around it (usually air), making a wave of squeezed-together and spread-out regions. This wave travels outward and reaches your ear, where you hear it as sound. The key idea is this: the particles do not travel to you — they only jiggle in place. What travels to you is the disturbance and the energy it carries. No particles in between (a vacuum) means no way to pass the disturbance along, so no sound. Get this one picture clear, and pitch, loudness, echoes, and even SONAR all fall into place.

How Sound is Produced

Let us start at the very beginning. Where does sound come from?

Take a rubber band, stretch it across an open box, and pluck it. You hear a sound. Watch the band closely — it is shivering, blurring back and forth. Now wait. As soon as the band goes still, the sound stops too. The sound lasts exactly as long as the shaking lasts.

This shaking has a name: vibration. A vibration is just a fast to-and-fro motion of an object about its rest position. Pluck a string, strike a steel plate, blow across a flute — in every case something is vibrating. The vibrating thing is called the source of the sound.

Even your own voice works this way. Put two fingers gently on the front of your throat and hum. You can feel it buzzing. Inside your throat are two stretched flaps of muscle called vocal cords. When air from your lungs rushes past them, they vibrate and make sound. Your tongue, lips and mouth then shape that sound into words.

Figure 10.1 shows two simple ways to see vibrations making sound.

The figure below pulls together two classic demonstrations, so look at both panels.

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A tuning fork (panel b) is a handy tool for sound experiments. It is a U-shaped steel bar with two arms called prongs and a handle called the stem. You hold the stem, tap a prong on a soft rubber pad, and it gives a clean, steady note. The prongs vibrate too fast for your eyes to follow — but touch a vibrating prong to water and the ripples give it away.

How Sound Travels: It Needs a Medium

We now know sound is made. But how does it reach you from the source?

Sound clearly travels through air — you hear voices across a room. But does it travel through other things too? Try this. Put your ear flat against a desk while a friend gently scratches the far end of the desk. You hear the scratch loud and clear through the wood. Now do it with water: tap two metal spoons together under the surface of a bucket of water — you still hear the clink. So sound travels through solids, liquids and gases.

The stuff that sound travels through is called a medium. A medium can be a solid, a liquid or a gas. Sound goes from its source to you through a medium.

This raises a sharp question. What if there were no medium at all between you and the source — just empty space with nothing in it? Empty space with no matter in it is called a vacuum. Would you still hear the sound?

The bell-jar experiment — and why vacuum is silent

To test this, scientists use the bell-jar experiment. An electric bell is hung inside a sealed glass jar. Switch it on, and you hear it ringing loudly. Now a vacuum pump slowly sucks the air out of the jar. As the air thins out, the sound gets fainter and fainter. When almost all the air is gone (a near vacuum), you can see the bell hammer still hitting — but you hear almost nothing.

Figure 10.2 shows the before-and-after of this experiment side by side.

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So why is a vacuum silent? Here is the reason, and it is the heart of the whole chapter.

Sound travels because a vibrating source pushes the particles next to it. Those particles bump into the next particles, which bump into the next, and so on — passing the disturbance along like a message down a line of people. Take away the particles, and there is no one to pass the message. In a vacuum there are no particles at all, so the disturbance simply cannot travel. No medium, no sound.

This is exactly why two astronauts on a spacewalk cannot hear each other or hear metal clanking, even right next to each other. Outer space is a near vacuum. They have to talk through radios fitted in their suits instead.

What a Sound Wave Really Is

We keep saying sound travels as a “disturbance” or a “wave”. Let us look closely at what that wave actually is.

Picture a long slinky — that springy coil toy — laid out on the floor, with a friend holding the far end. Give your end a sharp push toward your friend and then pull it back. You will see a region where the coils bunch up travel along the slinky to your friend. If you push-and-pull many times, you get a whole series of bunched-up regions moving along.

Here is the magic. Put a marker on one coil and watch it. That coil does not travel down the slinky. It only shuffles a little back and forth about its own spot. The bunching pattern races along, but the coils stay home. This is exactly how sound moves through air.

Compressions and rarefactions

To make it precise, imagine a long tube of air with a piston (a tight-fitting disc) at one end that we can push in and pull out.

• When the piston pushes in, it shoves the air particles in front of it together. This makes a small region where particles are crowded and the air is denser than usual. A high-density region like this is called a compression (C).
• When the piston pulls out, the particles near it spread apart, leaving a region where the air is thinner than usual. A low-density region like this is called a rarefaction (R).

Push and pull the piston over and over, and you get compressions and rarefactions following one after another, travelling down the tube. That is a sound wave.

Figure 10.3 puts the whole picture together — study it carefully, because everything else builds on it.

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So the formal definition is: a sound wave is a disturbance made of alternating compressions and rarefactions moving through a medium, without the particles of the medium themselves flowing along. The direction the wave travels is called the direction of propagation.

When the source is out in the open (not in a tube), the compressions and rarefactions spread out in all directions as expanding spheres, like the ripples on a pond but in 3-D.

Longitudinal and Transverse Waves

Look again at Figure 10.3. Which way do the air particles vibrate compared to the way the wave travels? They vibrate back and forth along the same line as the wave moves. The vibration is parallel to the direction the wave travels.

A wave where the particles vibrate parallel to the direction the wave travels is called a longitudinal wave. A sound wave is a longitudinal wave.

There is another type. In a transverse wave, the particles vibrate at right angles (perpendicular) to the direction the wave travels — think of flicking a rope up and down while the wave runs along it sideways. Light is a transverse wave.

Figure 10.4 contrasts the two clearly.

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There is one more important word here. A wave that needs a material medium to travel is called a mechanical wave. Sound is a mechanical wave — that is why it cannot cross a vacuum. Light is not mechanical (it is an electromagnetic wave), which is why sunlight reaches us across the empty space between the Sun and Earth, but the Sun’s roar never does.

Drawing a Sound Wave as a Graph

Compressions and rarefactions are hard to draw with dots every time. There is a neater way: a graph.

At any instant, the density of the medium changes as you move along the wave — high at a compression, low at a rarefaction. We plot distance along the x-axis and density up the y-axis. The average (normal) density is drawn as a horizontal dashed line. The curve rises above the line at a compression and dips below it at a rarefaction.

• The highest point of the curve (peak density, at the centre of a compression) is called a crest.
• The lowest point of the curve (least density, at the centre of a rarefaction) is called a trough.

Figure 10.5 shows how the dotted particle picture turns into this smooth graph.

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This graph is just a convenient way to draw a sound wave. A tall crest means a strong compression; a deep trough means a strong rarefaction.

Characteristics of a Sound Wave

Every sound wave can be described by a few measurable quantities. Let us meet them one by one. We will lean on a couple of earlier-class ideas, so here is a quick refresher first.

Wavelength, frequency and time period

Wavelength is the distance between two consecutive crests (or two consecutive troughs) of the wave. It is the length of one complete repeat of the pattern. We write it with the Greek letter λ (lambda). Its SI unit is the metre (m).

Now fix your attention on one single point in the medium and watch the density there. It keeps swinging from maximum (crest) to minimum (trough) and back to maximum. One full swing — max to min and back to max — is called one complete oscillation.

• Frequency is the number of these oscillations at a fixed point in one second. We write it with the Greek letter ν (nu). Its SI unit is per second, also called the hertz (Hz). So 50 Hz means 50 oscillations every second.
• Time period is the time taken for one complete oscillation. We write it T. Its SI unit is the second (s).

Frequency and time period are opposites of each other. If each oscillation takes a short time, then many fit into one second — so a short time period means a high frequency. The exact link is:

ν = 1 / T

Figure 10.6(a) shows what wavelength and time period look like on the graph.

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Let us put these numbers to work.

Amplitude and intensity

Look again at Figure 10.6(b). Both waves have the same wavelength, but one is “taller” than the other. That height has a meaning.

Amplitude is the maximum change in density of the medium in a compression (or rarefaction) compared with the average density. On the graph it is the height of a crest above the dashed average line. A bigger change in density means a bigger amplitude.

Amplitude is tied to energy. A wave with a larger amplitude carries more energy. You can see this in real life: strike a drum gently and it is quiet; strike it hard and it is loud — because you put more energy in, giving the wave a larger amplitude.

A related quantity is intensity: the amount of sound energy passing each second through a unit area held at right angles to the wave’s direction. As a wave spreads out from its source, the same energy is shared over a bigger and bigger area, so the intensity drops with distance. That is why a far-off sound is faint.

Speed of sound

The speed of sound is how fast the disturbance (a crest, say) travels through the medium.

Here is a neat result we can prove. In one time period T, the wave moves forward by exactly one wavelength λ (because that is one full repeat). Speed is distance ÷ time, so:

v = λ / T

But we know ν = 1 / T, so 1/T can be replaced by ν. This gives the most important formula of the chapter:

v = λ × ν

speed = wavelength × frequency

The speed of sound depends on the medium. Sound travels fastest in solids, slower in liquids, and slowest in gases. Roughly, it is about 4–5 times faster in water than in air, and about 15–20 times faster in steel than in air. Why? Figure 10.7 shows the reason.

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So the deeper reason is about how quickly particles can pass the push to their neighbours. In a solid the particles are crammed close and tightly bonded, so the disturbance is relayed almost instantly. In a gas the particles are far apart, so it takes longer.

The speed of sound in air also rises a little with temperature and humidity. For example, in dry air it is about 331 m/s at 0 °C and about 344 m/s at 22 °C. Importantly, in a given medium the speed is fixed — it does not depend on the frequency. If you change the frequency, the wavelength adjusts to keep v = λ × ν true, but the speed stays the same.

How we perceive sound: pitch and loudness

The quantities above (frequency, wavelength, amplitude, speed) are physical and measurable. But how a sound feels to us is a bit different. Two everyday words describe this experience.

Pitch is how we perceive frequency. A shrill, sharp sound — a whistle, a siren — is high-pitched and has a high frequency. A deep, rumbling sound — thunder, a big drum — is low-pitched and has a low frequency.

Loudness is how we perceive amplitude. A large-amplitude wave sounds loud; a small-amplitude wave sounds soft. Loudness also falls as you move away from the source. Loudness is measured in decibels (dB): rustling leaves are a few dB, normal talking about 60 dB, and firecrackers can cross 100 dB. Unwanted or harmful sound is called noise, and too much of it (noise pollution) can damage hearing and health.

Let us compare these two pairs of ideas side by side.

Humans can only hear a limited range of frequencies, called the audible range: about 20 Hz to 20,000 Hz (20 kHz). This range shrinks as we get older.

• Sound below 20 Hz is called infrasonic (or infrasound). Elephants can sense it; we cannot.
• Sound above 20 kHz is called ultrasonic (or ultrasound). Dogs, cats, bats and dolphins can hear it; we cannot.

Reflection of Sound: Echo and Reverberation

Sound waves bounce off hard surfaces, just as a ball bounces off a wall. This bouncing is the reflection of sound. Sound obeys the same laws of reflection you learned for light: the incoming sound and the reflected sound make equal angles with the normal (the line drawn at 90° to the surface), and all three lie in one plane.

Echo — and why a wall must be far enough

Shout near a hill, a cliff, or in a long empty corridor, and a moment later you hear your own voice again. That repeat is an echo — sound that reflected off a distant hard surface and came back.

But you do not hear an echo in a small room. Why not? It comes down to a limit of our hearing. Our brain can only tell two sounds apart if they arrive at least 0.1 second apart. If the reflected sound comes back sooner than 0.1 s after the original, the two merge and we hear just one sound.

This gives a way to find the minimum distance a wall must be to give a clear echo. In 0.1 s, sound (at 340 m/s) travels:

distance = speed × time = 340 m/s × 0.1 s = 34 m

But that 34 m is the round trip — to the wall and back. So the wall itself must be at least half of that: 17 m away. Figure 10.8 makes this clear.

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Echoes are clearest from hard, smooth surfaces, which reflect sound well. Soft surfaces like curtains absorb sound, and rough surfaces scatter it, so neither gives a sharp echo.

Reverberation

In a big hall, sound can bounce off many walls, the ceiling and the floor, again and again. These repeated reflections make the sound persist for a while even after the source has stopped. This lingering of sound by many quick reflections is called reverberation. It happens when the reflections arrive close together (less than about 0.05 s apart), so they blur into a continuous trailing sound rather than separate echoes.

Too much reverberation makes speech and music sound muddy. So auditoriums and concert halls are designed with sound-absorbing materials — soft panels, padded chairs, curtains — to soak up extra reflections and keep the sound clear.

Ultrasound, Infrasound and SONAR

Sounds outside our hearing range turn out to be hugely useful.

Ultrasonic waves (above 20 kHz) are used to image babies and internal organs without surgery (ultrasonography), to break up kidney stones, to clean delicate machine parts, and to find hidden cracks inside metal blocks. Infrasonic waves (below 20 Hz) travel huge distances and are used to detect earthquakes, volcanic eruptions and severe storms.

Echolocation and SONAR

A bat flies in total darkness without bumping into anything. It sends out short bursts of ultrasound and listens for the echoes that bounce back off walls and insects. From the echoes, the bat works out where things are. Finding objects using reflected sound like this is called echolocation. Dolphins and whales do it too.

Humans copied this idea for the sea. SONAR (Sound Navigation And Ranging) sends ultrasonic waves down into the water and listens for the reflection off the sea bed, a submarine, or a shipwreck. By timing the round trip, it finds how far away the object is. Figure 10.9 shows how it works.

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The crucial step in any SONAR or echo sum is remembering to use half the total time, because the wave travels the distance twice.

Common Mistakes

A few traps catch students again and again. Read these carefully.

Quick Check

Test yourself before moving on.

Practice Problems

Try each yourself before opening the solution.

Easy

Medium

Challenge

Summary

You can now explain:

• How sound is produced — every sound comes from a vibrating object (the source); when the vibration stops, the sound stops.
• Why sound needs a medium — sound travels by particles passing the disturbance to their neighbours, so a vacuum (no particles) is silent. This is why sound is called a mechanical wave, and why astronauts cannot hear each other in space.
• What a sound wave is — a series of compressions (high density) and rarefactions (low density) travelling through a medium, while the particles only vibrate in place. Sound is a longitudinal wave.
• The characteristics of a wave — wavelength (λ), frequency (ν, in Hz), time period (T, with ν = 1/T), amplitude, and speed, linked by v = λ × ν; and why sound is fastest in solids and slowest in gases.
• How we perceive sound — pitch comes from frequency, loudness from amplitude; and the human audible range is 20 Hz to 20 kHz, with infrasound below and ultrasound above.
• Reflection of sound — echoes (needing a surface at least 17 m away) and reverberation, and how halls are designed to control them.
• Applications — echolocation by bats and SONAR by ships, using the round-trip time of reflected ultrasound (depth = v × t / 2).

What’s Next

You have seen how a non-living wave like sound carries information and even helps life — bats hunting, dolphins navigating. The next big question is about life itself: how does life keep going, generation after generation? In Chapter 11 — Reproduction: How Life Continues, you will explore how living things make more of their own kind, from the simplest single cells to plants and animals. Just as a sound wave passes a pattern along without the particles travelling, reproduction passes on the pattern of life from parents to offspring.